Classical

Set Theory and Algebra MCQ - Sets

16:  

In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ?

A.

18

B.

36

C.

24

D.

None of these

 
 

Option: C

Explanation :


17:  

Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?

A.

p2

B.

p x q

C.

p + q

D.

2 pq

 
 

Option: B

Explanation :


18:  

The set of all Equivalence classes of a set A of cardinality C

A.

has the same cardinality as A

B.

forms a partition of A

C.

is of cardinality 2C

D.

is of cardinality C2

 
 

Option: B

Explanation :


19:  

Let Z denote the set of all integers.
Define f : Z —> Z by
f(x) = {x / 2 (x is even)
            0     (x is odd)
then f is

A.

onto but not one-one

B.

one-one but not onto

C.

one-one and onto

D.

neither one-one nor-onto

 
 

Option: A

Explanation :


20:  

Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is

A.

symmetric but not transitive

B.

partial order

C.

equivalence relation

D.

anti symmetric and not transitive

 
 

Option: C

Explanation :




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